Factorization of interest rate swap variation

ABSTRACT

Methods are described for processing and clearing derivative products such as interest rate swaps (IRSs). A swap value factor (SVF) may be generated to calculate the mark-to-market value of an IRS. The SVF may be a function of interest rates derived from a yield curve. Cash flow may be generated between the buyer and the seller to reflect the change in the market price of the derivative, i.e., the mark-to-market process. The results of a cleared swap may be used to determine or alter the margin deposit required by the buyer or seller.

The present application is a continuation of U.S. patent applicationSer. No. 11/950,117 filed Dec. 4, 2007 and claims priority to U.S.Provisional Patent Application No. 60/910,568 filed Apr. 6, 2007, theentire disclosures of which are hereby incorporated by reference.

FIELD OF THE INVENTION

The invention relates to trading and clearing of financial instruments.In particular, aspects of the invention relate to processing andclearing interest rate swaps.

BACKGROUND

Over-the-counter (OTC) products include financial instruments that arebought, sold, traded, exchanged, and/or swapped between counterparties.Many OTC derivatives exist to fill a wide range of needs forcounterparties, including limiting or mitigating exposure to risksand/or maximizing cash flow. After an exchange of an OTC product,counterparties may expend resources managing the product for theduration of its life. Management may be complicated based on the numberof exchanges and/or the specific terms of the contract.

An interest rate swap (IRS) is an example of a type of OTC product wherethe parties agree to exchange streams of future interest payments basedon a specified principal or notional amount. Each stream may be referredto as a leg. Swaps are often used to hedge certain risks, for instance,interest rate risk. They can also be used for speculative purposes.

An example of a swap includes a plain fixed-to-floating, or “vanilla,”interest rate swap. The vanilla swap includes an exchange of intereststreams where one stream is based on a floating rate and the otherinterest stream is based on a fixed rate. In a vanilla swap, one partymakes periodic interest payments to the other based on a variableinterest rate. The variable rate may be linked to a periodically knownor agreed upon rate for the term of the swap such as the LondonInterbank Offered Rate (LIBOR).

In return for the stream of payments based on the variable rate, theother party may receive periodic interest payments based on a fixedrate. The payments are calculated over the notional amount. The firstrate is called variable, because it is reset at the beginning of eachinterest calculation period to the then current reference rate, such asLIBOR published rate. The parties to an IRS swap generally utilize theseexchanges to limit, or manage, exposure to fluctuations in interestrates, or to obtain lower interest rates than would otherwise beunobtainable.

Usually, at least one of the legs to a swap has a variable rate. Thevariable rate may be based on any agreed upon factors such as areference rate, the total return of a swap, an economic statistic, etc.Other examples of swaps include total return swaps, and Equity Swaps.

A total return swap (also known as total rate of return swap, or TRORS)is a swap where one party receives interest payments based on anunderlying asset (plus any capital gains/losses) over the paymentperiod, while the other receives a specified fixed or floating cashflow. The total return is the capital gain or loss, plus any interest ordividend payments. The specified fixed or floating cash flow istypically unrelated to the credit worthiness of the reference asset. Theunderlying asset may be any asset, index, or basket of assets. Theparties gain exposure to the return of the underlying asset, withouthaving to actually hold the asset. That is, one party gains the economicbenefit of owning an asset without having the asset on its balancesheet, while the other (which does retain that asset on its balancesheet) has protection against a potential decline in its value. Anequity swap is a variation of a total return swap. The underlying assetin an equity swap may be a stock, a basket of stocks, or a stock index.

The expiration or maturity of the future streams of payments may occurwell into the future. Each party may have a book of existing and newIRSs having a variety of maturity dates. The parties may expendsubstantial resources tracking and managing their book of IRSs and otherOTC products. In addition, for each IRS, the party maintains an elementof risk that one of its counterparties will default on a payment.

Currently, financial institutions such as banks trade interest ratepayments and/or IRSs OTC. Steams of future payments must be valued todetermine a current market price. The market value of a swap is the sumof the difference between the net present value (NPV) of the futurefixed cash flows and the floating rate.

It would be desirable to provide a system and method for managing acentrally cleared international monetary market (IMM) dated swap suchthat the mark-to-market (MTM) process for the IMM dated swap issimplified while considering the variation amounts inherent in IMM datedswaps.

SUMMARY

Systems and methods are described for more conveniently processing andclearing derivative products such as interest rate swaps (IRSs). Thesystem generally includes clearing a swap having pre-defined parameters.For example, a standard IRS contract may include standard parameters forfloating rates, payment calendars, reset frequencies, day-countconventions for fixed and floating rates, etc. Clearing of a swapgenerally includes having a central clearing party for the swap. Theclearing party may act as the counterparty to each participant of anIRS, such that the clearing party compensates each party to the IRSaccording to, among other things, notional value, net-present value ofan IRS, and changes to the interest rate.

In another aspect of the invention, other types of swap products otherthan interest rate swaps may be used in accordance with variousembodiments of the invention.

In another aspect of the invention, a swap value factor (SVF) may begenerated to calculate the mark-to-market value of an IRS. The SVF maybe a function of interest rates derived from a yield curve.

In yet another aspect of the invention, a computer system configured toprocess and clear derivative products such as IRSs may receive aperformance bond (or margin) deposit from a buyer and seller of thederivative product. Subsequently, both buyer and seller may be requiredto mark-to-market and pay any losses or collect any profits with respectto the current market price of the derivative on an interval, e.g.,daily basis. Cash flow may be generated between the buyer and the sellerto reflect the change in the market price of the derivative, i.e., themark-to-market process. The results of the cleared swap may be used todetermine or alter the margin deposit required by the buyer or seller.

The details of these and other embodiments of the present invention areset forth in the accompanying drawings and the description below. Otherfeatures and advantages of the invention will be apparent from thedescription and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may take physical form in certain parts and steps,embodiments of which will be described in detail in the followingdescription and illustrated in the accompanying drawings that form apart hereof, wherein:

FIG. 1 illustrates a computer network system that may be used toimplement aspects of the invention.

FIG. 2 illustrates a mark-to-market calculation for an interest rateswap using a swap value factor in accordance with an aspect of theinvention.

FIGS. 3 and 4 illustrate exemplary yield curve information which may beused in accordance with various aspects of the invention.

FIGS. 5-7 illustrate a mark-to-market example for a three year interestrate swap in accordance with aspects of the invention.

FIGS. 8-10 illustrate additional exemplary yield curve information whichmay be used in accordance with various aspects of the invention.

FIGS. 11-14 illustrate a mark-to-market example for a three monthinterest rate swap in accordance with aspects of the invention.

FIGS. 15-36 illustrate a mark-to-market example for a thirty yearinterest rate swap in accordance with aspects of the invention.

FIG. 37 illustrates a flow diagram to determine the mark-to-market valueof an interest rate swap product in accordance with an aspect theinvention.

DETAILED DESCRIPTION

An example of a suitable operating environment in which various aspectsof the invention may be implemented is shown in FIG. 1. The operatingenvironment is only one example of a suitable operating environment andis not intended to suggest any limitation as to the scope of use orfunctionality of the invention. The processing unit 106 of computersystem 102 executes computer-executable instructions in accordance withaspects of the invention. Memory unit 104 may store computer-executableinstructions, which are executed by the computer system 102. Thecomputer-executable instructions may be comprised of modules inaccordance with aspects of the invention.

The computer system 102 may have one or more input/output devices 110(e.g., keyboard, mouse, voice automation, screen, kiosk, handheldcomputing device display, voice, etc.). Database 114 may be athird-party database containing, for example, information such as theLIBOR rate or other information useful in determining market values ofderivative products. The database 114 may be connected through wired orwireless communication networks to the computer system 102. Computingdevice 108 may be a laptop computer, handheld computing device, or anyother mobile computing device. In one embodiment in accordance with theinvention, a user of computing device 108 can remotely communicate viathe Internet to computer system 102 at a clearinghouse or exchange. Theuser may remotely enter orders for agreements offered by the exchangeand indicate a bank account to pay margin requirements and receive cashflows from swaps.

Of course, numerous additional servers, computers, handheld devices,personal digital assistants, telephones and other devices may also beconnected to exchange computer system 102. Moreover, one skilled in theart will appreciate that the topology shown in FIG. 1 is merely anexample and that the components shown in FIG. 1 may be connected bynumerous alternative topologies.

In accordance with various aspects of the invention, a clearinghouse mayact as a guarantor of the agreement for the derivative. At least onebenefit of an exchange traded derivative, as opposed to the OTC type, isthat the derivative is cleared and guaranteed by the clearinghouse. Thismay promise more interesting capital efficiencies for institutions thatmay cross-margin one derivative against another derivative.

In an aspect of the invention, upon execution of an IRS between parties,a clearing process may be initiated to process the cash flows resultingfrom the transaction. The clearing process may be initiated by, forexample, the processing unit 106 of computer system 102. Following theinitial cash flow processing, the clearing process maintains the IRSswaps, now-guaranteed by the central clearing party, for its lifespan,e.g., 10 years. As the IRS positions for all parties may bestandardized, the floating rate reset and payment processing may besimpler and easier to manage because there is only one floating ratereset and cash flow calendar per currency. The International Swaps andDerivatives Association (ISDA) day-count conventions, affect of holidaysand other cash flow and reset related parameters may also bepre-selected.

In another aspect of the invention, an IRS value at a particular datemay be calculated to determine the IRS's market value. The IRS value maybe determined by, for example, the processing unit 106 of computersystem 102. The below illustrative example assumes that swaps areforward starting to the nearest six month IMM date, and that the couponpayment frequency is also six months. Those skilled in the art willrealize that this is the convention used for Euro denominated swaps andthat USD denominated swaps are forward to the nearest three month IMMdate with a three month coupon frequency. Although the belowillustrative example may change slightly for USD denominated swaps, thegeneral concepts stated below are also applicable to USD denominatedswaps.

Table 1 illustrates an exemplary yield curve. As those skilled in theart will realize, IMM dates are typically Wednesdays but for the belowillustrative example Mondays have been utilized. The swap yields in aswap yield curve are the swap rates of market swaps of given tenors. Forinstance, to value a February 2008 IMM swap—i.e. a swap that terminateson the IMM date in February 2008—as of Feb. 12, 2007 (assumed to be theFebruary 2007 IMM date), the Table 1 yield curve may be utilized. Thoseskilled in the art will realize that various interest rate curves suchas LIBOR swap curves may be used. In addition, other interest ratecurves such as curves based on Eurodollars or Treasuries may also beutilized.

TABLE 1 Dates Yield Curve IMM Discount Factor Monday, Feb. 12, 20075.3450% df0 Monday, Aug. 13, 2007 5.4000% df1 Monday, Feb. 11, 20085.4150% df2

The rate of 5.4000% on Aug. 13, 2007 (the August 2007 IMM date), may bethe fixed swap rate associated with a six month swap which terminates onAug. 13, 2007. Similarly, the rate of 5.4150% on Feb. 11, 2008 (theFebruary 2008 IMM date), may be the fixed swap rate of a one year swapwhich terminates on Feb. 11, 2008. The yield curve used to value a oneyear swap may be built using fixed swap rates for the six month and oneyear market swaps. Both these swap yields may map to discount factors,which yield the present value, on Feb. 12, 2007, of a $1.00 cash flowoccurring on a specific date on the yield curve. The discount factor forFeb. 12, 2007, df0, will be 1, because this is the start date. Once df0is known, the discount factors for the remaining dates in the curve, df1and df2, may be obtained.

In another aspect of the invention, swaps cleared through aclearinghouse may use a yield curve that is based off of Swapstream'send of day settlements. In addition, the fixed cash flows associatedwith a fixed leg of IRS with a notional value of $1.00 may berepresented by:

$\begin{matrix}{C_{fixed} = {\sum\limits_{i = 1}^{n}\left\lbrack {\tau \times \left( {d_{i} - d_{i - 1}} \right)_{{ACT}/360} \times {df}_{i}} \right\rbrack}} & {{EQUATION}\mspace{14mu} 1}\end{matrix}$

Wherein the variable definitions may be defined as follows:

-   -   τ is the fixed rate on the swap.    -   “n” is the total number of fixed coupons included in the swap    -   d_(i) is the payment date of the i^(th) cash flow    -   ACT/360 refers to the daycount basis->the number of days between        coupon payments, divided by 360.    -   df_(i) is the discount factor of the i^(th) cash flow        (discounting back to the IMM start date)

The cash flows associated with a floating leg of an IRS may berepresented by:

$\begin{matrix}{C_{float} = {\sum\limits_{i = 1}^{n}\left\lbrack {r_{0.5}^{{di} - 1} \times \left( {d_{i} - d_{i - 1}} \right)_{{ACT}/360} \times {df}_{i}} \right\rbrack}} & {{EQUATION}\mspace{14mu} 2}\end{matrix}$

Wherein the variable definitions may be defined as follows:

-   -   “n” is the total number of floating coupons included in the swap    -   d_(i) is the payment date of the i^(th) cash flow    -   r_(0.5) ^(di-1) is the six month floating (LIBOR) rate at        d_(i-1)    -   ACT/360 refers to the daycount basis        -   Actual number of days per month and 360 days per year for            all daycount fractions        -   Therefore, the number of years in a six month period            consisting of 182 days=182/360    -   df_(i) is the discount factor of the i^(th) cash flow

Floating cash flow may also be represented as following:

$\begin{matrix}\begin{matrix}{C_{float} = {\sum\limits_{i = 1}^{n}\left\lbrack {r_{0.5}^{{di} - 1} \times \left( {d_{i} - d_{i - 1}} \right)_{{ACT}/360} \times {df}_{i}} \right\rbrack}} \\{= {{df}_{0} - {df}_{n}}}\end{matrix} & {{EQUATION}\mspace{14mu} 3}\end{matrix}$

Where the variable definitions may be defined as follows:

-   -   C_(float) is the discounted sum of floating cash flows    -   df₀ is 1 (present value of $1.00 cash flow occurring on,        February 12^(th))    -   df_(n) is the discount factor associated with the n^(th) cash        flow

In another aspect of the invention, an expression for the discountfactors may be derived. The discount factors may be derived by, forexample, the processing unit 106 of computer system 102. At the time ofrate fixing (i.e. at the time of settlement), the NPV of the swap iszero. Therefore, the discounted sum of the fixed cash flows (Equation 1)equals the discounted sum of the floating cash flows (Equation 2):

$\begin{matrix}{{\sum\limits_{i = 1}^{n}\left\lbrack {\tau \times \left( {d_{i} - d_{i - 1}} \right)_{{ACT}/360} \times {df}_{i}} \right\rbrack} = {\sum\limits_{i = 1}^{n}\left\lbrack {r_{0.5}^{{di} - 1} \times \left( {d_{i} - d_{i - 1}} \right)_{{ACT}/360} \times {df}_{i}} \right\rbrack}} & {{EQUATION}\mspace{14mu} 4}\end{matrix}$

Using Equation 3, the right side of Equation 4 equals df₀−df_(n).Therefore, Equation 4 becomes:

${\sum\limits_{i = 1}^{n}\left\lbrack {\tau \times \left( {d_{i} - d_{i - 1}} \right)_{{ACT}/360} \times {df}_{i}} \right\rbrack} = {{df}_{0 -}{df}_{n}}$

Splitting up the summation on the left side of the equation aboveyields:

${{\sum\limits_{i = 1}^{n - 1}\left\lbrack {\tau \times \left( {d_{i} - d_{i - 1}} \right)_{{ACT}/360} \times {df}_{i}} \right\rbrack} + \left\lbrack {\tau \times \left( {d_{n} - d_{n - 1}} \right)_{{ACT}/360} \times {df}_{n}} \right\rbrack} = {{df}_{0 -}{df}_{n}}$

Simplifying yields:

${{df}_{n}\left\lbrack {1 + {\tau \times \left( {d_{n} - d_{n - 1}} \right)_{{ACT}/360}}} \right\rbrack} = {{df}_{0 -}{\sum\limits_{i = 1}^{n - 1}\left\lbrack {\tau \times \left( {d_{i} - d_{i - 1}} \right)_{{ACT}/360} \times {df}_{i}} \right\rbrack}}$

Solving for df_(n) yields:

$\begin{matrix}{{df}_{n} = \frac{{df}_{0 -}{\sum\limits_{i = 1}^{n - 1}\left\lbrack {\tau \times \left( {d_{i} - d_{i - 1}} \right)_{{ACT}/360} \times {df}_{i}} \right\rbrack}}{\left( {1 + {\tau \times \left( {d_{n} - d_{n - 1}} \right)_{{ACT}/360}}} \right)}} & {{EQUATION}\mspace{14mu} 5}\end{matrix}$

Where the variable definitions may be defined in Equation 5 as follows:

-   -   df_(n) is the n^(th) IMM discount factor in yield curve (to be        solved for)    -   “n” is the number of fixed coupons in the swap's tenor    -   df₀ is equal to 1, as it is the present value of $1.00 today,        the IMM valuation date    -   τ is the fixed rate on the swap    -   d_(i) is the payment date of the i^(th) cash flow        -   (d_(i)−d_(i-1)) is the number of fractional years between            payment dates, on an ACT/360 basis.    -   df_(i) is the i^(th) discount factor, discounting back to the        IMM start date

In another aspect of the invention, the swap NPV may be calculated bydiscounting the swap's cash flows back to spot. Each of the IMM discountfactors (which represent the present value of a $1.00 coupon cash flow,discounted back to the IMM start date of the swap) may be discountedback to spot. In an embodiment, the spot discount factor of the “n^(th)”coupon cash flow may be represented as sf_(n). The spot discount factormay be calculated as follows:

$\begin{matrix}{{sf}_{n} = \frac{{df}_{n}}{\left( {1 + {r_{IMM}^{OIS} \times {{Stub\_ days}/360}}} \right)}} & {{EQUATION}\mspace{14mu} 6A}\end{matrix}$

In an alternative embodiment of the discounting methodology, the spotdiscount factor on the “n^(th)” coupon cash flow may be represented assf_(n) and calculated as follows:

$\begin{matrix}{{sf}_{n} = \frac{{df}_{n}}{\left\lbrack {1 + {r_{IMM}^{OIS} \times \left( {1/360} \right)}} \right\rbrack^{{({{{IMM}\mspace{14mu} {date}} - {{Spot}\mspace{14mu} {date}}})}{{ACT}/360}}}} & {{EQUATION}\mspace{14mu} 6B}\end{matrix}$

Those skilled in the art will realize that Equation 6A employs a simpleinterest based discounting methodology. This is conducive to single cashflow instruments such as OIS swaps (the OIS swap has a single cash flowassociated with it that occurs upon maturity of the swap). Withreference to the Equation 6A, the fact that the interest rate in thedenominator is multiplied by the fractional number of years in theperiod is indicative of the usage of simple interest based discounting.

Furthermore, as those skilled in the art will realize Equation 6Billustrates an alternative embodiment of the discounting methodologywhich employs a compound interest based discounting method. This methodmay be conducive to an instrument that has cash flows that span multipleperiods during the life of the instrument. Each cash flow is reinvestedupon receipt, thereby creating the effect of earning interest oninterest->i.e. compound interest. In Equation 6B, the fact that the(1+r) interest rate term in the denominator is raised to the exponent ofthe fractional number of years in the period is indicative of compoundinterest based discounting.

In the following detailed description of the invention, as the OISinstrument in the current implementation of this product has a singlecash flow, simple interest based discounting is used. However, as thoseskilled in the art will realize, one may extend the methodology toemploy compound interest based discounting.

In Equations 6A and 6B, the variable definitions may be defined asfollows:

-   -   df_(n) is the IMM discount factor of the n^(th) coupon of the        swap. In other words, it is the present value (discounted back        to the IMM start date of the swap) occurring on the swap's        n^(th) coupon date.    -   r_(IMM) ^(OIS) is the fixed rate on an overnight indexed swap        (OIS), for a given day. OIS swaps will be traded on the        Swapstream platform and will mature on the next IMM date. These        rates are settled daily—as such, r_(IMM) ^(OIS) is the interest        rate that prevails between the spot date and the IMM date, which        makes it useful for discounting from the IMM date back to spot.        Because r_(IMM) ^(OIS) as quoted is an annual rate, it is        multiplied by 1/360 to yield a daily rate (following the ACT/360        daycount convention). The benefits of using the OIS swap fixed        rate for spot discounting may include:        -   The highly liquid nature of OIS swaps make them a viable            instrument to obtain spot discount rates from.        -   Providing a standardized discounting method that all            interested parties can use to value the swap product.    -   Stub_days divided by 360 is the number of fractional years        between the spot date and the IMM valuation date. This is the        actual number of days in the stub period, and is therefore on an        ACT/360 basis. For instance, if there are 3 days between spot        and the IMM date, then Stub_days/360=3/360.    -   Note that (IMM date—Spot date) in equation 6B and “Stub_days” in        equation 6A are used interchangeably.

In an aspect of the invention, a swap value factor (SVF) may becalculated to simplify the mark-to-market (MTM) variation calculation ofan interest rate swap. The SVF may include the swap's applicablediscount factors and associated daycount fractions into a single factor.The SVF may be a function of interest rates derived from yield curves.

For example, a clearinghouse or other entity may wish to calculate theMTM variation of a six month USD swap (i.e. a swap with two quarterlycoupons—swap matures in September 2007) that commences on Mar. 19, 2007with a notional swap value of $1.00 dollar. For this exemplary scenario,the current date is assumed to be Mar. 16, 2007 with an IMM start dateof Mar. 19, 2007. The MTM variation of the swap maturing in September2007 may be calculated as of the end of the day settlement on Mar. 16,2007 relative to Mar. 15, 2007, end of day settlement. In this exemplaryscenario, the Mar. 15, 2007 settlement rate for the swap maturing inSeptember 2007 is 5.38% and the Mar. 16, 2007 settlement rate is 5.40%.The calculated number of days between the Mar. 19, 2007 (the next IMMdate) start date and June 2007 coupon is 91 days. The calculated numberof days between the June 2007 coupon and the September 2007 coupon is 92days. The discount factors used to discount the September 2007 swap'scoupon back to Mar. 15 and Mar. 16, 2007 along with the coupon daycountsare illustrated in Table 2.

TABLE 2 Days between Mar. 16, 2007 Coupon coupons Discount Factor June2007 91 0.9891 September 2007 92 0.9775

The MTM on Mar. 16, 2007 may be calculated using the equation asillustrated in FIG. 2. As shown in FIG. 2, the MTM 202 of an interestrate swap (per $1 swap notional value, calculated at time “T” relativeto time “T−t”), using a SVF at time “T” 204 may be calculated. Applyingthe equation:

MTM=[(Sep-07 Settlement Rate on 3/16/07)−(Sep-07 Settlement Rate on3/15/07)]*(Swap Value Factor on 3/16/07).

The swap value factors in the above illustrative scenario may bedetermined by calculating the MTM variation on the September 2007 swapusing the following method:

MTM=(Fixed NPV of Sep-07 using 3/16/07 settlement)−(Fixed NPV of Sep-07using 3/15/07 settlement)

This relationship holds true since the NPV of the fixed cash flows=theNPV of the floating cash flows at any given settlement. The Fixed NPV ofa swap on a given day is the present value of all its coupon cash flows.

Substituting numerical values per the data above:

MTM=(5.40%)*($1.00)*(91/360)*(0.9891)+(5.40%)*($1.00)*(92/360)*(0.9775)−[(5.38%)*($1.00)*(91/360)*(0.9891)+(5.38%)*($1.00)*(92/360)*(0.9775)]

MTM=(5.40%)*[(91/360)*(0.9891)+(92/360)*(0.9775)]−(5.38%)*[(91/360)*(0.9881)+(92/360)*(0.9775)]

The daycount fractions (i.e. 91/360 and 92/360) are used above becausethe fixed settlement rates are annual rates—for a given coupon, theywould only apply on a fractional basis as given by the daycount fraction(e.g. 91/360 for the June 2007 coupon in this example->the denominatoris 360 since the daycount convention being followed is ACT/360).

The discount factors listed above discount the cash flows back to thedates March 15th and March 16th. The discount factors derived from theswap curve would only discount back to the IMM date of March 19th. Inorder to discount back from March 19th to each of March 15th and March16th, stub discount rates are required. It is assumed that all necessarystub discounting has been done in arriving at the discount factors givenabove.

Based on the above, the Swap Value Factor may be expressed as

[(91/360)*(0.9891)+(92/360)*(0.9775)]

In accordance with an aspect of the invention, the swap value factor fora given day may be calculated as the (daycount fraction*discount factor)product summed over the swap's coupons.

FIGS. 3 and 4 illustrate exemplary yield curve information which may beused in accordance with various aspects of the invention. For example,the exemplary yield curves shown in FIGS. 3 and 4 may be used in thecalculation of a three year interest rate swap as illustrated in FIGS.5-7 in accordance with aspects of the invention. Additionally, FIGS. 5-7illustrate that the mark-to-market calculation using the SVFs areequivalent to the mark-to-market calculation using the traditionalvaluation methodology.

In FIG. 3, an exemplary yield curve 302 shown in table format isillustrated for May 30, 2007. Similarly, FIG. 4 illustrates an exemplaryyield curve 402 in table format for May 31, 2007.

Table 3 illustrated below details inputs for use in an exemplarycalculation of a mark-to-market value using SVFs for a three year swap.In Table 3, the last market date is shown to be Wednesday, May 30, 2007,the current date is shown as Thursday, May 31, 2007, and the forward IMMstart date of the swap is Monday, Jun. 18, 2007.

TABLE 3 Input Value Last Mark Date Wednesday, May 30, 2007 TodayThursday, May 31, 2007 Forward IMM Start Date Monday, Jun. 18, 2007Notional Amount of Swap $1,000,000,000.00 OIS Swap Rate on May 30, 20078.6532% Days between May 30, 2007 and 19.0000 Jun. 18, 2007 OIS SwapRate on May 31, 2007 8.6531% Days between May 31, 2007 and 18.0000 Jun.18, 2007 Jun-10 CME Swap Settlement Rate 6.7530% on May 31, 2007 Jun-10CME Swap Settlement Rate 6.7530% on May 30, 2007

FIG. 5 illustrates the calculation of a fixed NPV on May 30, 2007 for athree year interest rate swap using a swap value factor in accordancewith an aspect of the invention. As shown in FIG. 5, a fixed NPV 501 of$185,549,800.56 may be calculated as of May 30, 2007 for a swap with anotional value 503 of $1,000,000,000. A SVF 502 may be calculated havinga numerical value of 2.7476647499 which is the sum of the coupon valuefactors 504. Each of the coupon value factors which may be calculated onthe coupon expiration dates may be calculated as the product of theDaycount Fraction 506 and the Spot Discount Factor 508.

FIG. 6 illustrates the calculation of a fixed NPV on May 31, 2007 for athree year interest rate swap using a swap value factor in accordancewith an aspect of the invention. As shown in FIG. 6, a fixed NPV 601 of$185,549,800.56 may be calculated as of May 31, 2007 for a swap with anotional value 603 of $1,000,000,000. A SVF 602 may be calculated havinga numerical value of 2.7476647499 which is the sum of the coupon valuefactors 604. Each of the coupon value factors which may be calculated onthe coupon expiration dates may be calculated as the product of theDaycount Fraction 606 and the Spot Discount Factor 608. As shown in FIG.6, the mark-to-market value on May 31, 2007 relative to May 30, 2007 of$0.00 “612” may be calculated by subtracting the calculated swap NPVsarrived at by using the May 31^(st) and May 30^(th) settlement prices.

FIG. 7 verifies the accuracy of the mark-to-market valuation (calculatedusing the swap value factors) for a three year swap on May 31, 2007relative to May 28, 2007 in accordance with an aspect of the invention.In FIG. 7, the coupons are discounted back to an IMM date using IMMdiscount factors 702. Using the IMM discount factors 702, present valuesof the coupons 704 may be determined. Net present values discounted backto June 18^(th) (forward IMM date) of $186,352,591.05 “706” and$186,352,591.05 “708” may be calculated. The net present valuecalculations “706” and “708” may be discounted from the June 18^(th)forward IMM date to the spot date of May 31^(st). A mark-to-market valueon May 31, 2007 relative to May 30, 2007 of $0.00 “710” may becalculated by subtracting the calculated swap NPVs arrived at by usingMay 31^(st) and May 30^(th) settlement prices.

FIGS. 8-10 illustrate exemplary yield curve information which may beused in accordance with various aspects of the invention. FIGS. 11-36illustrate additional exemplary mark-to-market values for differentinterest rate swaps of varying durations in accordance with variousaspects of the invention.

In particular, FIGS. 11-14 illustrate exemplary MTM calculations usingswap value factors for a three month swap on Mar. 14, 2007 relative toMar. 13, 2007 in accordance with an aspect of the invention.

FIGS. 15-36 illustrate exemplary MTM calculations using swap valuefactors for a thirty year swap in accordance with an aspect of theinvention. Those skilled in the art will realize that any swap durationmay be utilized and will fall within the methodology of the describedaspects of the invention.

FIG. 37 illustrates a flow diagram to determine the mark-to-market valueof an interest rate swap product at a time T₂ relative to an earliertime T₁ in accordance with an aspect the invention. In a first step3702, a swap value factor may be determined by a central clearing party.In an embodiment, the central clearing party may be a clearing house.The swap value factor may encapsulate at least one discounting factorassociated with the interest rate swap into a single swap value factor.The swap value factor may be a sum of coupon value factors.

In an aspect of the invention, each coupon value factor may becalculated for a coupon expiration date as a product of a daycountfraction and spot discount factor. The daycount fraction may be thenumber of days from the IMM start date of the swap until first coupondate divided by 360.

In another aspect of the invention, the spot discount factor may becalculated using the equation (equation 6A above):

${sf}_{n} = \frac{{df}_{n}}{\left( {1 + {r_{IMM}^{OIS} \times {{Stub\_ days}/360}}} \right)}$

As those skilled in the art will realize, this equation uses a simpleinterest based discounting methodology. Such a simple interestdiscounting method may be conducive to single cash flow instruments suchas OIS swaps (the OIS swap has a single cash flow associated with itthat occurs upon maturity of the swap).

In an alternative embodiment, the spot discount factor may also becalculated by using the equation, (as discussed above equation 6B):

${sf}_{n} = \frac{{df}_{n}}{\left\lbrack {1 + {r_{IMM}^{OIS} \times \left( {1/360} \right)}} \right\rbrack^{{({{{IMM}\mspace{14mu} {date}} - {{Spot}\mspace{14mu} {date}}})}{{ACT}/360}}}$

Those skilled in the art will realize Equation 6B illustrates analternative embodiment of the discounting methodology which employs acompound interest based discounting method. This method may be conduciveto an instrument that has cash flows that span multiple periods duringthe life of the instrument.

In step 3704, the mark-to-market value of the interest rate swap productat time T₂ relative to time T₁ may be calculated by subtracting asettlement price at T₁ from a settlement price at T₂ and multiplying thedifference by the swap value factor. Finally in step 3706, themark-to-market values may be displayed.

The present invention has been described herein with reference tospecific exemplary embodiments thereof. It will be apparent to thoseskilled in the art that a person understanding this invention mayconceive of changes or other embodiments or variations, which utilizethe principles of this invention without departing from the broaderspirit and scope of the invention as set forth in the appended claims.

1. A method comprising: determining a first discount factor for a financial instrument based on a yield curve, wherein the financial instrument is associated with a start date; generating, by a processor, a second discount factor for discounting the first discount factor from the start date back to a spot date; generating a swap value factor based on the second discount factor; determining a mark-to-market value for the financial instrument based on the swap value factor; and outputting the mark-to-market value.
 2. The method of claim 1, wherein the discounting of the first discount factor is based on an interest rate.
 3. The method of claim 2, wherein the interest rate is based on a time interval between the spot date and the start date.
 4. The method of claim 1, wherein the swap value factor is based on a sum of coupon value factors.
 5. The method of claim 4, wherein each of the coupon value factors is calculated for a corresponding coupon expiration date as a mathematical product of a daycount fraction and a coupon discount factor.
 6. The method of claim 5, wherein the daycount fraction is number of days between a coupon start date and the corresponding coupon expiration date divided by
 360. 7. The method of claim 1, wherein the interest rate is a daily interest rate.
 8. The method of claim 1, wherein the interest rate is based on a fixed rate of an overnight indexed swap.
 9. The method of claim 3, wherein the time interval is a number of days between the spot date and the start date.
 10. An apparatus comprising: a memory unit; and a processing unit coupled to the memory unit and configured to cause the apparatus at least to perform: determining a first discount factor for a financial instrument based on a yield curve, wherein the financial instrument is associated with a start date; generating a second discount factor for discounting the first discount factor from the start date back to a spot date; generating a swap value factor based on the second discount factor; determining a mark-to-market value for the financial instrument based on the swap value factor; and outputting the mark-to-market value.
 11. The apparatus of claim 10, wherein the discounting of the first discount factor is based on an interest rate.
 12. The apparatus of claim 11, wherein the interest rate is based on a time interval between the spot date and the start date.
 13. The apparatus of claim 10, wherein the swap value factor is based on a sum of coupon value factors.
 14. The apparatus of claim 13, wherein each of the coupon value factors is calculated for a corresponding coupon expiration date as a mathematical product of a daycount fraction and a coupon discount factor.
 15. The apparatus of claim 14, wherein the daycount fraction is number of days between a coupon start date and the corresponding coupon expiration date divided by
 360. 16. A memory containing computer-executable instructions for causing a computer device at least to perform: determining a first discount factor for a financial instrument based on a yield curve, wherein the financial instrument is associated with a start date; generating a second discount factor for discounting the first discount factor from the start date back to a spot date; generating a swap value factor based on the second discount factor; determining a mark-to-market value for the financial instrument based on the swap value factor; and outputting the mark-to-market value.
 17. The memory of claim 16, wherein the discounting of the first discount factor is based on an interest rate.
 18. The memory of claim 17, wherein the interest rate is based on a time interval between the spot date and the start date.
 19. The memory of claim 16, wherein the swap value factor is based on a sum of coupon value factors.
 20. The memory of claim 19, wherein each of the coupon value factors is calculated for a corresponding coupon expiration date as a mathematical product of a daycount fraction and a coupon discount factor. 